How Music and Mathematics Relate

Course Overview

Gain a new perspective on two of the greatest achievements of human culture—music and mathematics—and the unexpected connections that bind them together. Great minds have long sought to understand this relationship, as both involve patterns, structures, and relationships. Music serves as a fertile testing ground for mathematical principles, while mathematics explains the sounds instruments make and how composers create music. By exploring the mathematics of music, you’ll appreciate both fields, even without special abilities in either area—learning the mathematics behind tuning an instrument, understanding different musical traditions, and exploring modern sound technology.

Video Lectures

1. Overtones-Symphony in a Single Note – 50 min
   Analyze the harmonic series behind a single note and study the sounds produced by a range of instruments.
2. Timbre-Why Each Instrument Sounds Different – 46 min
   Investigate the concept of timbre and how it determines why different instruments sound unique.
3. Pitch and Auditory Illusions – 48 min
   Explore the way your brain fills in missing information to create auditory illusions.
4. How Scales Are Constructed – 48 min
   Learn the mathematics of musical scales and how they shape different musical traditions.
5. How Scale Tunings and Composition Coevolved – 46 min
   Compare historic and modern compositions, focusing on the mathematics of tuning.
6. Dissonance and Piano Tuning – 50 min
   Discover how dissonance can be quantified and learn to tune a piano using beats.
7. Rhythm-From Numbers to Patterns – 45 min
   Investigate the grouping of beats and its effect on rhythm, including polyrhythms.
8. Transformations and Symmetry – 50 min
   Explore how composers use mathematical techniques to transform melodies.
9. Self-Reference from Bach to Godel – 43 min
   Delve into the concept of self-reference in music and mathematics.
10. Composing with Math-Classical to Avant-Garde – 45 min
    Discover how some composers use mathematics to create their works.
11. The Digital Delivery of Music – 46 min
    Understand the mathematics behind digital audio technology and sound quality.
12. Math, Music, and the Mind – 48 min
    Explore the connections between mathematics, music, and the human mind.